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<b>let </b><font color="Maroon" title="c1">TS</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">PS</font>, <font color="Olive" title="b2">QS</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">TS</font>  st <font color="Olive" title="b1">PS</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a> &amp; <font color="Olive" title="b2">QS</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">PS</font> &amp; <font color="Olive" title="b2">QS</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> holds <br/><font color="Olive" title="b2">QS</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a></span><br/><b>let </b><font color="Maroon" title="c2">PS</font>, <font color="Maroon" title="c3">QS</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">TS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">PS</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a> &amp; <font color="Maroon" title="c3">QS</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">PS</font> &amp; <font color="Maroon" title="c3">QS</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> implies <font color="Maroon" title="c3">QS</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a> )</span><br/>





<b>assume </b><b>that </b><br/><a NAME="E1:14"/><i><font color="Green" title="E14">A1</font></i>: 
<font color="Maroon" title="c2">PS</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a>
 <b>and </b><br/><a NAME="E2:14"/><i><font color="Green" title="E15">A2</font></i>: 
<font color="Maroon" title="c3">QS</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">PS</font>
 <b>and </b><br/><a NAME="E3:14"/><i><font color="Green" title="E16">A3</font></i>: 
<font color="Maroon" title="c3">QS</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">QS</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:14_1"/>
( <font color="Maroon" title="c2">PS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c2">PS</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1"><b>suppose </b></a><a NAME="E1:14_1_1"/>
<font color="Maroon" title="c2">PS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">QS</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a></span><br/><div class="add"><a NAME="E2:14_1_1"/><b>then </b>
<font color="Maroon" title="c3">QS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">TS</font>
 <b>by </b><i><a class="txt" href="compts_1.html#E2:14"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="xboole_1.html#T3" title="XBOOLE_1:th.3">XBOOLE_1:3</a></i>;<br/><b>hence </b><a NAME="E3:14_1_1"/>
<font color="Maroon" title="c3">QS</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a>
 <b>by </b><i><a class="ref" href="compts_1.html#T9" target="_self" title="COMPTS_1:th.9">Th9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_2"><b>suppose </b></a><a NAME="E1:14_1_2"/><i><font color="Green" title="E17">A4</font></i>: 
<font color="Maroon" title="c2">PS</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">QS</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a></span><br/><div class="add"><a NAME="E2:14_1_2"/><i><font color="Green" title="E18">A5</font></i>: 
<font color="Maroon" title="c2">PS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">TS</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c2">PS</font></span>)</span>
 <b>by </b><i><a class="ref" href="pre_topc.html#D10" title="PRE_TOPC:def.10">PRE_TOPC:def 10</a></i>;<br/><a NAME="E3:14_1_2"/>
<font color="Maroon" title="c1">TS</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c2">PS</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>
 <b>by </b><i><a class="txt" href="compts_1.html#E1:14"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="compts_1.html#E1:14_1_2"><i><font color="Green" title="E17">A4</font></i></a>, <a class="ref" href="compts_1.html#T12" target="_self" title="COMPTS_1:th.12">Th12</a></i>;<br/><a NAME="E4:14_1_2"/><b>then </b>
for <font color="Olive" title="b1">QQ</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">TS</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c2">PS</font></span>)</span>  st <font color="Olive" title="b1">QQ</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">QS</font> holds <br/><font color="Olive" title="b1">QQ</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a>
 <b>by </b><i><a class="txt" href="compts_1.html#E3:14"><i><font color="Green" title="E16">A3</font></i></a>, <a class="ref" href="compts_1.html#T17" target="_self" title="COMPTS_1:th.17">Th17</a>, <a class="ref" href="tops_2.html#T34" title="TOPS_2:th.34">TOPS_2:34</a></i>;<br/><b>hence </b><a NAME="E5:14_1_2"/>
<font color="Maroon" title="c3">QS</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a>
 <b>by </b><i><a class="txt" href="compts_1.html#E2:14"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="compts_1.html#E2:14_1_2"><i><font color="Green" title="E18">A5</font></i></a>, <a class="ref" href="compts_1.html#T11" target="_self" title="COMPTS_1:th.11">Th11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

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